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safari File Edit View History Bookmarks window Help M smartsite.ucdavis.edu a secure search McAfee Chegg Study I Guided Solutions and https://smartsite.ucdavis.edu/access/... SmartSite@UCDavis ARE 100B A01-A Suppose Callaway prices the C-Tec high 2. Figure 9.12 Price 20 18 16 14 12 10 8 Quantity Reference: Ref 9-14 (Figure 9.12) Suppose the firm\'s demand curve for its product increases from D1 to D2. The firm\'s marginal cost is given by MC-50 a. Solve for the change in the profit-maximizing quantity resulting from the increase in demand. b. Solve for the change in the profit-maximizing price resulting from the increase in demand.

Solution

a) When the firm\'s demand curve is at D₁ , the firms revenue will be = Price X quantity demanded

Revenue at D₁ = $ 10 X 4 units

Revenue at D₁ = $ 40

When the firm\'s demand curve is at D₂ , the firms revenue will be = $ 15 X 6

Revenue at D₂ = $ 90

The marginal revenue when the demand curve shifts from D₁ to D₂ = $ 90 - $ 40

Marginal revenue of the firm = $ 50

Equating marginal revenue = marginal cost

MR = MC

$ 50 = 5Q

Q = 10 units ( The profit maximizing quantity resulting from the increase in demand )

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b) The profit maximizing price is when marginal revenue = marginal cost

Marginal revenue = P { ( 1+ (1/e_p ) }

e_p = price elasticity of demand

e_p = % change in quantity demanded / % change in price

from Demand curve D₁ to D₂ , the % change in quantity demanded = 50%

% change in price from Demand curve D₁ to D₂ = 50 %

e_p = 50% / 50%

e_p = 1 ( unitary elastic)

P { ( 1+ (1/e_p ) } = 5Q

The profit maximizing quantity = 10 units ; Marginal cost = 5Q

Marginal cost = 5 X 10

Marginal cost = $ 50

P ( 1 + 1/1 ) = 5 X 10

P ( 2) = 50

P = $ 25

The profit maximizing price resulting from the increase in demand = $ 25 .